Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Filtered Multiplicative Bases of Restricted Enveloping Algebras

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Avaliação da posição condilar e disfunção temporomandibular em pacientes com má oclusão de Classe II submetidos à protrusão mandibular ortopédica

OBJETIVO: avaliar a participação da protrusão mandibular ortopédica e da posição condilar na prevalência de sinais e sintomas de disfunção temporomandibular (DTM). METODOLOGIA: a amostra foi composta por 60 indivíduos divididos em 3 grupos, sendo o grupo I correspondente a indivíduos não tratados; o grupo II composto por jovens em tratamento com o Bionator; e o grupo III por jovens já tratados com este aparelho. Os indivíduos da amostra responderam a um questionário relativo aos principais sintomas de DTM, permitindo a classificação dos mesmos de acordo com a presença e severidade dessas disfunções. Esses jovens também se submeteram à avaliação da movimentação mandibular, palpação dos músculos mastigatórios e inspeção de ruídos articulares. Radiografias transcranianas padronizadas das ATMs direita e esquerda foram realizadas, para obtenção do grau de concentricidade condilar. RESULTADOS: os testes ANOVA, Kruskal-Wallis e qui-quadrado foram utilizados para análise dos dados. De acordo com os resultados do questionário anamnésico, 66,67% da amostra foram classificados com ausência de DTM; 30% com DTM leve e apenas 3,33% com DTM moderada, sem diferença entre os grupos estudados (p > 0,05). Quanto à concentricidade condilar, o grupo II apresentou os valores de menor concentricidade (côndilos mais anteriorizados), com diferença estatisticamente significante em relação ao grupo I (p < 0,05). Uma associação entre a concentricidade condilar e a prevalência de DTM, no entanto, não foi encontrada. CONCLUSÃO: a protrusão ortopédica, apesar de alterar a posição dos côndilos, não aumentou a prevalência de DTM na população estudada.

As técnicas NASVD e MNF e sua aplicação na redução de ruídos em dados gamaespectrométricos

A desintegração radioativa é um processo aleatório e a estimativa de todas as medidas associadas é governada por leis estatísticas. Os perfis de taxas de contagem são sempre "ruidosos" quando utilizados períodos curtos como um segundo para cada medida. Os filtros utilizados e posteriormente as correções feitas no processamento atual de dados gamaespectrométricos não são suficientes para remover ou diminuir, consideravelmente, o ruído oriundo do espectro. Dois métodos estatísticos que atuam diretamente nos dados coletados, isto é, nos espectros, vêm sendo sugeridos na literatura para remover e minimizar estes ruídos remanescentes o Noise-Adjusted Singular Value Decomposition - NASVD e Maximum Noise Fraction - MNF. Estes métodos produzem uma redução no ruído de forma significativa. Neste trabalho eles foram implementados dentro do ambiente de processamento do software Oasis Montaj e aplicados na área compreendida pelos blocos I e II do levantamento aerogeofísico que recobre a porção oeste da Província Mineral do Tapajós, entre os Estados do Pará e Amazonas. Os dados filtrados e não-filtrados com as técnicas de NASVD e MNF foram processados com os parâmetros e constantes fornecidos pela empresa Lasa Engenharia e Prospecções S.A., sendo estes comparados. Os resultados da comparação entre perfis e mapas apresentaram-se de forma promissora, pois houve um ganho na resolução dos produtos.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

Recursive linear estimation for general discrete-time descriptor systems

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Convergence of the associated Riccati recursion and stability properties of the steady-state filter are provided. (C) 2010 Elsevier Ltd. All rights reserved.

Root Water Extraction under Combined Water and Osmotic Stress

Using a numerical implicit model for root water extraction by a single root in a symmetric radial flow problem, based on the Richards equation and the combined convection-dispersion equation, we investigated some aspects of the response of root water uptake to combined water and osmotic stress. The model implicitly incorporates the effect of simultaneous pressure head and osmotic head on root water uptake, and does not require additional assumptions (additive or multiplicative) to derive the combined effect of water and salt stress. Simulation results showed that relative transpiration equals relative matric flux potential, which is defined as the matric flux potential calculated with an osmotic pressure head-dependent lower bound of integration, divided by the matric flux potential at the onset of limiting hydraulic conditions. In the falling rate phase, the osmotic head near the root surface was shown to increase in time due to decreasing root water extraction rates, causing a more gradual decline of relative transpiration than with water stress alone. Results furthermore show that osmotic stress effects on uptake depend on pressure head or water content, allowing a refinement of the approach in which fixed reduction factors based on the electrical conductivity of the saturated soil solution extract are used. One of the consequences is that osmotic stress is predicted to occur in situations not predicted by the saturation extract analysis approach. It is also shown that this way of combining salinity and water as stressors yields results that are different from a purely multiplicative approach. An analytical steady state solution is presented to calculate the solute content at the root surface, and compared with the outputs of the numerical model. Using the analytical solution, a method has been developed to estimate relative transpiration as a function of system parameters, which are often already used in vadose zone models: potential transpiration rate, root length density, minimum root surface pressure head, and soil theta-h and K-h functions.

Strategies for genetic model specification in the screening of genome-wide meta-analysis signals for further replication

Background Meta-analysis is increasingly being employed as a screening procedure in large-scale association studies to select promising variants for follow-up studies. However, standard methods for meta-analysis require the assumption of an underlying genetic model, which is typically unknown a priori. This drawback can introduce model misspecifications, causing power to be suboptimal, or the evaluation of multiple genetic models, which augments the number of false-positive associations, ultimately leading to waste of resources with fruitless replication studies. We used simulated meta-analyses of large genetic association studies to investigate naive strategies of genetic model specification to optimize screenings of genome-wide meta-analysis signals for further replication. Methods Different methods, meta-analytical models and strategies were compared in terms of power and type-I error. Simulations were carried out for a binary trait in a wide range of true genetic models, genome-wide thresholds, minor allele frequencies (MAFs), odds ratios and between-study heterogeneity (tau(2)). Results Among the investigated strategies, a simple Bonferroni-corrected approach that fits both multiplicative and recessive models was found to be optimal in most examined scenarios, reducing the likelihood of false discoveries and enhancing power in scenarios with small MAFs either in the presence or in absence of heterogeneity. Nonetheless, this strategy is sensitive to tau(2) whenever the susceptibility allele is common (MAF epsilon 30%), resulting in an increased number of false-positive associations compared with an analysis that considers only the multiplicative model. Conclusion Invoking a simple Bonferroni adjustment and testing for both multiplicative and recessive models is fast and an optimal strategy in large meta-analysis-based screenings. However, care must be taken when examined variants are common, where specification of a multiplicative model alone may be preferable.

Interaction between Tobacco and Alcohol Use and the Risk of Head and Neck Cancer: Pooled Analysis in the International Head and Neck Cancer Epidemiology Consortium

Background: The magnitude of risk conferred by the interaction between tobacco and alcohol use on the risk of head and neck cancers is not clear because studies have used various methods to quantify the excess head and neck cancer burden. Methods: We analyzed individual-level pooled data from 17 European and American case-control studies (11,221 cases and 16,168 controls) participating in the International Head and Neck Cancer Epidemiology consortium. We estimated the multiplicative interaction parameter (psi) and population attributable risks (PAR). Results: A greater than multiplicative joint effect between ever tobacco and alcohol use was observed for head and neck cancer risk (psi = 2.15; 95% confidence interval, 1.53-3.04). The PAR for tobacco or alcohol was 72% (95% confidence interval, 61-79%) for head and neck cancer, of which 4% was due to alcohol alone, 33% was due to tobacco alone, and 35% was due to tobacco and alcohol combined. The total PAR differed by subsite (64% for oral cavity cancer, 72% for pharyngeal cancer, 89% for laryngeal cancer), by sex (74% for men, 57% for women), by age (33% for cases < 45 years, 73% for cases > 60 years), and by region (84% in Europe, 51% in North America, 83% in Latin America). Conclusions: Our results confirm that the joint effect between tobacco and alcohol use is greater than multiplicative on head and neck cancer risk. However, a substantial proportion of head and neck cancers cannot be attributed to tobacco or alcohol use, particularly for oral cavity cancer and for head and neck cancer among women and among young-onset cases. (Cancer Epidemiol Biomarkers Prev 2009;18(2):541-50)

Alcohol and tobacco, and the risk of cancers of the upper aerodigestive tract in Latin America: a case-control study

Cancers of the upper aerodigestive tract (UADT; including oral cavity, pharynx, larynx and oesophagus) have high incidence rates all over the world, and they are especially frequent in some parts of Latin America. However, the data on the role of the major risk factors in these areas are still limited. We have evaluated the role of alcohol and tobacco consumption, based on 2,252 upper aerodigestive squamous-cell carcinoma cases and 1,707 controls from seven centres in Brazil, Argentina, and Cuba. We show that alcohol drinkers have a risk of UADT cancers that is up to five times higher than that of never-drinkers. A very strong effect of aperitifs and spirits as compared to other alcohol types was observed, with the ORs reaching 12.76 (CI 5.37-30.32) for oesophagus. Tobacco smokers were up to six times more likely to develop aerodigestive cancers than never-smokers, with the ORs reaching 11.14 (7.72-16.08) among current smokers for hypopharynx and larynx cancer. There was a trend for a decrease in risk after quitting alcohol drinking or tobacco smoking for all sites. The interactive effect of alcohol and tobacco was more than multiplicative. In this study, 65% of all UADT cases were attributable to a combined effect of alcohol and tobacco use. In this largest study on UADT cancer in Latin America, we have shown for the first time that a prevailing majority of UADT cancer cases is due to a combined effect of alcohol and tobacco use and could be prevented by quitting the use of either of these two agents.

The SARS algorithm: detrending CoRoT light curves with Sysrem using simultaneous external parameters

Surveys for exoplanetary transits are usually limited not by photon noise but rather by the amount of red noise in their data. In particular, although the CoRoT space-based survey data are being carefully scrutinized, significant new sources of systematic noises are still being discovered. Recently, a magnitude-dependant systematic effect was discovered in the CoRoT data by Mazeh et al. and a phenomenological correction was proposed. Here we tie the observed effect to a particular type of effect, and in the process generalize the popular Sysrem algorithm to include external parameters in a simultaneous solution with the unknown effects. We show that a post-processing scheme based on this algorithm performs well and indeed allows for the detection of new transit-like signals that were not previously detected.

Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.